Classical theory of stationary nucleation

Volmer and Weber [2.14], Farkas [2.15] and Kaischew and Stranski [2.16-2.18] were the first who examined the stationary nucleation kinetics and derived theoretical expressions for the stationary nucleation rate. However, in this Chapter we shall present the results of the more rigorous treatments of Becker and Doring [2.6] and ofZeldovich [2.19] and Frenkel [2.20] who laid the foundations of the contemporary classical nucleation theory (see also [2.V-2.9] and [2.21-2.24]). For the sake of simplicity we shall neglect both the line tension effects (equations (1.42) and (1.70)) and the dependence of the specific free surface energy on the size of the clusters (equation (1.43). 

In the frameworks of the classical nucleation theory the size n of the clusters is considered as a continues variable, the nucleation work is expressed by equation (1.65) and the sum in equation (2.15) is replaced by an integral, i.e.. 

After that the integral is olved on three simplifying assumptions  

Under these conditions the integral in equation (2.16) transforms into  

Let us assume that a metastable equilibrium can be established in the supersaturated parent phase. In this case the constant flux of clusters through the size axis equals zero and equations (2.8) transform into  

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